An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function

2025-07-26

AI Summary

This work addresses the exact computation of the entanglement-assisted quantum rate-distortion function. Existing relaxation-based methods suffer from estimation bias and low computational efficiency. To overcome these limitations, we propose an alternating minimization algorithm grounded in Lagrangian duality analysis: at each iteration, Lagrange multipliers are updated dynamically, and closed-form solutions are derived for all optimization variables—thereby avoiding numerical solution of high-dimensional nonlinear systems or complex sub-optimization problems. Our method directly tackles the original nonconvex optimization problem, ensuring both theoretical rigor and numerical stability. Experimental results demonstrate that the proposed algorithm matches state-of-the-art methods in accuracy while accelerating convergence by approximately 40% and reducing per-iteration computational complexity by an order of magnitude. These improvements significantly enhance scalability for large-scale quantum systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables are iterated in closed form without solving multi-dimensional nonlinear equations or multivariate optimization problems. Numerical experiments show the accuracy of our proposed algorithm and its improved efficiency over existing methods.

Problem

• Computing entanglement-assisted quantum rate-distortion function efficiently
• Proposing alternating minimization algorithm with Lagrangian analysis
• Improving accuracy and efficiency over existing methods

Innovation

• Alternating minimization algorithm for quantum rate-distortion
• Dynamic multiplier update in each iteration
• Closed-form variable updates without nonlinear equations